Time and Date Stamps (logged): 05:12:07 12-05-2008
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Precalculus II
University Physics (Phy 231, Phy 241) Test 2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
A ball has a horizontal range of 21 meters when it is projected horizontally from an
altitude of 17 meters. What will be its range if it is projected at an angle of 8 degrees
below horizontal with the same initial speed? Approximately how much does its horizontal
range change per degree from horizontal?
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Problem Number 2
A ball of mass .4 kg is tossed vertically upward from altitude 6.8 meters and allowed
to rise to a maximum altitude of 7.42 meters before falling to an altitude of 6.81 meters.
- Determine the work done by gravity on the ball and the work done by the ball against
gravity as it rises from its initial to its maximum altitude, and determine its kinetic
energy change during that displacement.
- Using energy considerations determine its initial velocity.
- Determine the work done by gravity on the ball and the work done by the ball against
gravity between its release at the 6.8 meter altitude and its final position at the 6.81
meter altitude.
- Determine the change in kinetic energy between these positions, and use energy
considerations to determine its velocity at the final position.
- How are the work done by the ball and its kinetic energy change related?
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Problem Number 3
If a mass of 4 kg moving at 8 m/s collides with a mass of 9 kg moving at -3
m/s, and the two masses are 'stuck together' after collision, then what is their common
velocity after collision? Is this collision possible for the system consisting of
the two masses without the conversion of some internal source of potential energy?
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Problem Number 4
Coasting from rest down a certain hill, whose slope is variable, I reach a speed
of 13.92 m/s at the bottom. If I coast from rest down the second half of the hill I
reach a speed of 13 m/s. Ignoring the effects of air resistance and friction:
- How fast would I therefore be going if I coasted from rest down the first half of
the hill?
- How high would I have to climb from the halfway point reach the top?
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Problem Number 5
Derive the expression for v(r), the velocity of a satellite orbiting at distance
r from a planet of mass M. Find dv / dr.
- Given that the mass of a certain neutron star is about 6 * 10^30 kg and G = 6.67
* 10^-34 J s, what is the velocity of a circular orbit at a distance of 20 km from
the center of the star?
- What is dv / dr at this distance?
- Use these results estimate of the velocity change between the given orbit and an
orbit at a distance of 20 km + 14.5 meters from the center of the star.
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Problem Number 6
A ball slides down a frictionless ramp of length L to the end of the ramp, which
protrudes over the edge of a table, and falls freely the remaining distance `dy to the
floor. The vertical change in elevation on the ramp is h.
- What is the horizontal range range(h) of the ball?
- What is d / dh (range(h))?
- For a ramp of length 35 cm, vertical rise 9 cm and a vertical fall `dy = 55 cm,
according to a differential estimate by how much would the range be expected to change if
h changed by .2 cm?
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Problem Number 7
A disk of negligible mass and radius 16 cm is constrained to rotate on a frictionless
axis about its center. The disk remains in a vertical plane with its axis horizontal. On
the disk are mounted masses of 9 grams at a distance of 11.68 cm from the center, 16 grams
data distance of 7.84 cm from the center and 32 grams at a distance of 6.24 cm from the
center. A force is applied at the rim of the disk by a mass of 71.25 grams attached to by a
light string around the rim.
- As the mass descends 119 cm, with the disk originally at rest, by how much does the
potential energy of the system change?
- What therefore will be the angular velocity attained by the disk and the velocity
attained by the descending mass?
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Problem Number 8
Sketch and label force diagrams for each of the following situations:
A mass of 35 grams is attached to a cart of mass 140 grams and suspended over a pulley
of negligible mass and friction. The cart is placed on a ramp whose slope is just enough
to compensate for the small frictional force acting on the cart. When the system is
released, what will be the acceleration of the cart?
Answer the same question if the cart is placed on a ramp making an angle of 7 degrees
with horizontal, with the cart being pulled down the ramp, and if the frictional force is
.018 times the normal force on the cart.
If after adding an unknown mass to the cart on the 7 degree incline the acceleration
of the system is 33.06 cm/s^2, what is the unknown mass?